To integrate x*e^(x^2 /2) do I have to use Integration by parts
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To integrate x*e^(x^2 /2) do I have to use Integration by parts

[From: ] [author: ] [Date: 11-12-20] [Hit: ]
......
from what I saw, integration by parts was the only option. so i went ahead and let u = x and dv/dx = e^(x^2 /2). So i ended up getting du/dx = 1 and v = (e^(x^2 /2))/2 <--- however im not too sure if i got v correct since my CAS does not give me any answer when I integrate dv/dx.

Experts, please help

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∫ x e^(x²/2) dx
Put x² / 2 = u , => x dx = du
The given integral reduces to ∫ e^u du = e^u + const
= e^(x²/2) + const [ Restoring the value of u ]

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Try u-substitution with x^2/2 equaling u and du=x
integrate e^u du
1
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